Algebra 73 - Factoring Quadratics by inspection - part 1

The video tutorial explains how to factor quadratic expressions using the method of inspection. It begins with an introduction to factoring quadratics and special products, then delves into the trial and error process of factoring by inspection. Examples are provided to illustrate the method, including cases with no constant term and general cases with all non-zero constants. The tutorial also highlights the limitations of the inspection method and suggests alternative methods like completing the square or using the quadratic formula for more complex quadratics.

What is the primary goal when factoring a quadratic expression?

• To find the roots of the expression

• To convert it into a cubic expression

• To find a pair of linear expressions that multiply to the quadratic

• To simplify the expression

When is trial and error not needed in factoring a quadratic expression?

• When the quadratic is a perfect square

• When the quadratic has a constant term

• When the quadratic has no constant term

• When the quadratic is a difference of squares

In the expression 5X^2 - 2X, what are the linear factors?

• X and 5X - 2

• 5X and X - 2

• X and X - 5

• 5X and X + 2

What is the first step in factoring by inspection when the coefficient of X squared is one?

• Find the roots of the quadratic

• Determine the values of P and R

• Find values for Q and S that satisfy certain conditions

• Graph the quadratic function

What are the factors of the quadratic expression X^2 + 5X + 6?

• X + 3 and X + 4

• X + 2 and X + 3

• X + 1 and X + 6

• X + 2 and X + 4

What is the solution set for the quadratic equation X^2 + 5X + 6 = 0?

• -5 and -6

• 2 and 3

• -2 and -3

• 0 and 5

Why might factoring by inspection not be possible for some quadratics?

• The values of Q and S are not integers

• The quadratic is a perfect square

• The quadratic is a difference of squares

• The quadratic has no real zeros

What are the zeros of the quadratic function X^2 + 10X - 24?

• -2 and 12

• 10 and -24

• 2 and -12

• 0 and 10

What advanced methods can be used when factoring by inspection is not possible?

• Graphing and substitution

• Using logarithms and exponents

• Completing the square and using the quadratic formula

• Synthetic division and polynomial long division

What additional challenge arises when the coefficient of X squared is not one?

• The quadratic cannot be factored

• The quadratic becomes a cubic

• The values of Q and S are always negative

• We must also determine values for P and R